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Range of a function of a trig expression

This type of question, asked 3 times: 2021 Paper 24, 25 Jan 2023, 6 Apr 2024. All 3 questions below, oldest first.

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  1. Question 1

    2021 Paper 24

    77
    The range of the function, f(x)=log⁡5(3+cos⁡(3π4+x)+cos⁡(π4+x)+cos⁡(π4−x)−cos⁡(3π4−x))f(x) =\log_{\sqrt{5}}\left( 3 + \cos\left( \frac{3\pi}{4}+x \right)+ \cos\left( \frac{\pi}{4}+x \right)+ \cos\left( \frac{\pi}{4}-x \right)- \cos\left( \frac{3\pi}{4}-x \right) \right) is:

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  2. Question 2

    25 Jan 2023

    169
    Let f:R→Rf:R \rightarrow R be a function defined by f(x)=log⁡m{2(sin⁡x−cos⁡x)+m−2}f(x) =\log_{\sqrt{m}}\mathbf{\{}\sqrt{2}(\sin x - \cos x) + m - 2\}, for some mm, such that the range of ff is [0,2]\lbrack 0,2\rbrack. Then the value of mm is

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  3. Question 3

    6 Apr 2024

    166
    Let f(x)=17−sin⁡5xf(x) =\frac{1}{7 - \sin5x} be a function defined on RR. Then the range of the function f(x)f(x) is equal to:

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